Dynamic Analysis of Multiplex Networks With Hybrid Maintenance Strategies

The advent of smart terminals and the IOT era has prompted the emergence of the multiplex network system. With the rapid information transmission in multiplex networks, security incidents caused by malicious attackers occur frequently. In light of the foregoing, this paper concentrates on modeling and analyzing the propagation process of multiplex networks. Particularly, this paper proposes an epidemic-based RCMO (Running- Confined- Malfuntioned- Overhauled) model after considering the operating state of equipment and a class of visibility-aware malware. After that, the stability analysis of the equilibria is performed to verify the effectiveness of the propagation threshold obtained in RCMO. Then, we introduce static controls including unique control, target control, acquaintance control, and pulse control, as well as dynamic controls including continuous-time and pulsed forms to the suppression strategies for preventing the spread of malware. Furthermore, the control strategies are cross-combined into
$6\times 6$
hybrid maintenance strategies (HMS), and the simulation analysis is performed from three perspectives: evolution of state variables, accumulation of revenue, and change of controls. We discovered through experimental results that the optimal HMS to inhibit the propagation of malware and the HMS with the highest revenue are always different under various network topologies, but they are all hybrid combinations of continuous-time and pulse controls. To some extent, dynamic control can reduce discrepancies between the HMS and generate approximate returns. Finally, we propose a few cyber defense recommendations for network administrators.